where \(m^*\)  is the absolute value of the effective mass, \(E_F\)  is the Fermi energy and \(\Delta (\mathbf {r})=\Delta _0 \text{tanh}(r/\xi _V) e^{-i \theta }\)  with the size of a vortex core \(\xi _V\) . Notice that we consider a system with a hole like band character, as 2H-NbSe\(_2\)[1]}. Otherwise, the diagonal components of the matrix need to be interchanged. As \(\text{2H-NbSe}_2\)  is a strong type II superconductor with a large penetration depth (of about 200 nm [2]}, [3]}), we can take a constant magnetic field. Spin degeneracy is not included for simplicity, since the wave functions for both spin states are the same. Following previous works [4]}, [5]}, [6]}, the CdGM bound state energy and corresponding wave function in the asymptotic region (\(r \gg 1/k_F\) ) in the low energy limit are approximately given by
\(\varepsilon _n &= \frac{E_n}{\Delta _0}= (n+\frac{1}{2}) \frac{\Delta _0}{2E_F}, \\\psi _n(\mathbf {r}) &=\begin{pmatrix}\psi ^{+}_n(\mathbf {r})\\\psi ^{-}_n(\mathbf {r})\end{pmatrix} \\&= A_n(r)\begin{pmatrix}e^{-i (n+1)\theta } \cos (k_F r + F_n-\frac{\eta _n}{2})\\e^{-i n \theta } \cos (k_F r + F_n+\frac{\eta _n}{2})\end{pmatrix}. \nonumber \) 
